Question: All of the 4th grade teachers and students from Covington went on a field trip to an art museum. Tickets were $$6.00$ each for teachers and $$2.50$ each for students, and the group paid $$49.00$ in total. The next month, the same group visited a natural history museum where the tickets cost $$12.00$ each for teachers and $$9.50$ each for students, and the group paid $$143.00$ in total. Find the number of teachers and students on the field trips.
Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${6x+2.5y = 49}$ ${12x+9.5y = 143}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-2$ ${-12x-5y = -98}$ ${12x+9.5y = 143}$ Add the top and bottom equations together. $ 4.5y = 45 $ $ y = \dfrac{45}{4.5}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $ {6x+2.5y = 49}$ to find $x$ ${6x + 2.5}{(10)}{= 49}$ $6x+25 = 49$ $6x = 24$ $x = \dfrac{24}{6}$ ${x = 4}$ You can also plug ${y = 10}$ into $ {12x+9.5y = 143}$ and get the same answer for $x$ ${12x + 9.5}{(10)}{= 143}$ ${x = 4}$ There were $4$ teachers and $10$ students on the field trips.